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C₉×C₁₉×H(3,𝔽₃) #17987274

order	4617
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₁₉ · Schur multiplier (H₂) = C₃⁴

Aliases

C₉×C₁₉×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center	C₃×C₉×C₁₉	C₃²
commutator	C₃	C₃²×C₉×C₁₉
Frattini, cosocle	C₃²	C₃³×C₁₉
socle	C₃²×C₁₉	C₃³
prime radical	C₃×C₁₉×H(3,𝔽₃)	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₉ ◁ G

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1539

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(10,11,13)(12,15,17)(14,18,16);(11,14,15)(13,17,18)

Conjugacy classes & character table

1881 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	H(3,𝔽₃)⋊#10587018, #28353170, #28353700, …
maximal subgroup of	C₁₉×H(3,𝔽₃)⋊C₂₇, C₁₉×#10624453, C₁₉×#10624583, …
maximal normal subgroup of	C₁₉×H(3,𝔽₃)⋊C₂₇, C₁₉×#10624453, C₁₉×#10624583, …
maximal quotient of	C₉×C₁₉×C₃²⋊C₉, C₁₉×#10624555, C₁₉×#10624556, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 35);